Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T18:40:21.669Z Has data issue: false hasContentIssue false
  • English
  • Français

An analysis of two and three dimensional unsteady withdrawal flows, using shallow water theory

Published online by Cambridge University Press:  17 February 2009

A. J. Koerber  and
L. K. Forbes
A. J. Koerber
Affiliation:
Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia.
L. K. Forbes
Affiliation:
Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper examines the predictions of shallow water theory for steady and unsteady withdrawal flows through an extended sink from fluid of finite depth. Two-dimensional plane flows and three-dimensional axi-symmetric flow through a circular drain are examined. Shallow water theory indicates the presence of limiting configurations, where the surface of the fluid collapses directly into the sink. In addition, this theory suggests that some previously computed steady solutions may be unstable.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 3 , January 2000 , pp. 338 - 357
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Forbes, L. K. and Hocking, G. C., “Flow caused by a point sink in a fluid having a free surface”, J. Austral. Math. Soc. Ser. B 32 (1990) 231–249.CrossRefGoogle Scholar
[2]Forbes, L. K. and Hocking, G. C., “The bath-plug vortex”, J. Fluid Mech. 284 (1995) 43–62.CrossRefGoogle Scholar
[3]Forbes, L. K., Hocking, G. C. and Chandler, G. A., “A note on withdrawal through a point sink in fluid of finite depth”, J. Austral. Math. Soc. Ser. B 37 (1996) 406–416.CrossRefGoogle Scholar
[4]Hocking, G. C., “Flow from a vertical slot into a layer of finite depth”, Appl. Math. Modelling 16 (1992) 300–306.CrossRefGoogle Scholar
[5]Hocking, G. C. and Forbes, L. K., “Subcritical free-surface flow caused by a line source in a fluid of finite depth”, J. Engin. Math. 26 (1992) 455–466.CrossRefGoogle Scholar
[6]Ivey, G. N. and Blake, S., “Axisymmetric withdrawal and inflow in a density-stratified container”, J. Fluid Mech. 161 (1985) 115–137.CrossRefGoogle Scholar
[7]LeVeque, R. J., Numerical Methods for Conservation Laws (Birkhäuser Verlag, Basel; Boston; Berlin, 1990).CrossRefGoogle Scholar
[8]MacCormack, R. W., “Numerical solution of the interaction of a shock wave with a laminar boundary layer”, Phys. Fluids A 3 (1971) 2652–2658.Google Scholar
[9]Mekias, H. and Vanden-Broeck, J.-M., “Supercritical free-surface flow with a stagnation point due to a submerged source”, Phys. Fluids A 1 (1989) 1694–1697.CrossRefGoogle Scholar
[10]Mekias, H. and Vanden-Broeck, J.-M., “Subcritical flow with a stagnation point due to a source beneath a free surface”, Phys. Fluids A 3 (1991) 2652–2658.CrossRefGoogle Scholar
[11]Stoker, J. J., Water Waves (Interscience Publishers, Inc., New York, 1957).Google Scholar
[12]Tuck, E. O. and Vanden-Broeck, J.-M., “A cusp-like free-surface flow due to a submerged source or sink”, J. Austral. Math. Soc. Ser. B 25 (1984) 443–450.CrossRefGoogle Scholar
[13]Zhou, Q. and Graebel, W. P., “Axisymmetric draining of a cylindrical tank with a free surface”, J. Fluid Mech. 221 (1990) 551–532.CrossRefGoogle Scholar